Finite Group Databasebeta

C41×C22⋊(C13⋊C9) #34062893

order19188
automorphism?
homologyAbelianization (H1) = C9×C41 · Schur multiplier (H2) = C2

Aliases

direct productC41×C22⋊(C13⋊C9)
unambiguous semidirect productC22⋊(C41×C13⋊C9)
unambiguous semidirect productC13⋊(C22⋊C9×C41)
unambiguous semidirect product(C22×C41)⋊(C13⋊C9)
unambiguous semidirect product(C13×C41)⋊(C22⋊C9)

Splittings

derived, HallC22×C13 ⋊ C9×C41
HallC22×C13×C41 ⋊ C9
HallC13×C41 ⋊ C22⋊C9
HallC22×C41 ⋊ C13⋊C9
SylowC13 ⋊ C22⋊C9×C41
SylowC22 ⋊ C41×C13⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C41C22⋊(C13⋊C3)
commutator, hypocenterC22×C13C9×C41
FrattiniC3C41×C22⋊(C13⋊C3)
Fitting, socle, prime radicalC22×C3×C13×C41C3
cosocleC22×C3×C13C3×C41
LCSG ▷ C22×C13
UCSC1 ◁ C3×C41

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9594

Conjugacy classes & character table

2460 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19188, 45);